In conventional microlithographic exposure methods, a pattern of features defined by a reticle is illuminated and projected so as to form the pattern on a photosensitive substrate. (The substrate is typically coated with a photoresist or other photosensitive material which makes the substrate "photosensitive". Commonly, the photoresist is "positive" and has high thermal stability.) Upon exposure, a latent image-reaction density .xi. as defined in Equation (1) below is typically produced in the photoresist, according to the intensity I of the illuminating light reaching the substrate: EQU .xi.=exp(-CD), D=I.sup.m.multidot.t=J.multidot.t (1)
wherein t is the exposure time and C is a constant determined by the photosensitive material. The exponent m expresses the response dynamics of the photosensitive material relative to the incident light intensity, where m=1 denotes a linear response and m.noteq.1 denotes a non-linear response. As indicated, I.sup.m can be substituted with J, wherein J is the latent image density of the photoresist. PA1 wherein i.sub.0 is the modulation of the irradiance function of the object (mask) for a given spatial frequency, f is the transfer function of the optical system for a given spatial frequency (i.e., the optical transfer function "OTF"; also termed the "modulation transfer function" or "MTF"), and .nu. is the spatial frequency of the pattern on the mask. PA1 (wherein K.sub.2 is a process-dependent constant), these schemes proved to be impractical since they tended to reduce the DOF and/or increase the size and complexity of the optical system. In addition, the ultimate resolution limit of the photosensitive material could not exceed the resolution limit as dictated by the projection-optical system. PA1 wherein I.sub.0 (x) is the light-intensity distribution on the "object" (mask), F(x) is the focal intensity distribution F(x) of the projection optical system, x is the position coordinate on the photoresist, and * indicates convolution.
The modulation i(.nu.) of the irradiance function of the image for a given spatial frequency .nu. required to form a latent image in the photoresist, assuming spatially incoherent illumination, is given by: EQU i(.nu.)=i.sub.0 (.nu.).multidot.f(.nu.) (2)
The spatial frequency .nu..sub.0 at a threshold at which f becomes insignificant from a process viewpoint is expressed by the following equation, wherein .lambda. is the exposure wavelength, NA is the numerical aperture of the projection-optical system on the photoresist side, and K.sub.1 is a process constant: ##EQU1##
According to Equation (3), the resolution limit of the optical system (i.e., the highest spatial frequency .nu..sub.c that can be imaged by the optical system with incoherent illumination; sometimes termed the "cutoff frequency") is essentially determined by the numerical aperture NA and the exposure wavelength .lambda. (in which instance K.sub.1 =0.25): ##EQU2##
Thus, high resolution can be obtained by either increasing the numerical aperture NA and/or decreasing the exposure wavelength .lambda.. With these choices in mind, high-NA lenses were developed and various schemes were devised for exploiting short-wavelength light sources, such as excimer lasers, etc., in an effort to improve resolution. However, since the depth of focus ("DOF") of the projection-optical system is expressed by: ##EQU3##
An exposure method offering prospects of exceeding the exposure limit of the projection-optical system was proposed in Japanese Kokai (laid-open) patent document no. HEI 6-291009. To reproduce a pattern that exceeded the resolution limit of the projection-optical system, multiple exposures were performed on a substrate coated with a photoresist having a non-linear exposure-sensitivity characteristic. The latent-image reaction density with such a photoresist increased according to the m.sup.th power (m&gt;1) of the incident light intensity. The latent-image reaction density could also be increased by performing multiple exposures while (a) changing the exposure intensity distribution on the photoresist, or (b) displacing the reticle and substrate relative to each other by a specified amount between exposures, or (c) using a different reticle for each exposure. The consequences of the non-linear exposure-sensitivity are explained below.
In a conventional photolithography system as described above, the light-intensity distribution I(x) created on an image surface by incoherent illumination passing through the projection-optical system from a mask is given by:
I(x)=I.sub.0 (x)*F(x) (6)
Fourier-transform convolution yields Equation (7) which is the same as Equation (2): EQU i(.nu.)=i.sub.0 (.nu.).multidot.f(.nu.). (7)
Usually, .nu..sub.c =2NA/.lambda., as shown in Equation (4) above. A resolution that exceeds .nu..sub.c cannot be achieved. However, if, e.g., a photoresist exhibiting second-order (non-linear) response dynamics (wherein m=2 in Equation (1); termed a "two-photon-absorbing resist") is utilized, then the latent-image density exhibits a distribution J(x) according to the square of the exposure-intensity distribution I(x), substituted into Equation (6) as follows: EQU J(x)=(I(x)).sup.2 =[I(x)*F(x)].sup.2. (8)
Using Equation (7), the latent-image density distribution j for the given spatial frequency is expressed as: EQU j(.nu.)=[i.sub.0 (.nu.).multidot.f(.nu.)]*[i.sub.0 (.nu.).multidot.f(.nu.)]. (9)
In instances in which the exposure-density distribution exhibits, e.g., a sine profile, Equation (9) indicates that use of such a non-linear photoresist causes the sine profile to have more amplitude than when a linear (first-order) photoresist is used. Such an increase in amplitude of the latent-image density distribution increases the contrast of the resulting image formed in the photoresist.
Since the phase of the sine wave in the latent-density distribution is the same for both linear photoresists and non-linear photoresists, the cut-off frequency .nu..sub.c of the latent-image density remains unchanged. As a result, it is impossible to form fine patterns at a resolution greater than the resolution limit of the optical system.
The scheme disclosed in the Japan Kokai patent document no. HEI 6-291009 using non-linear photoresists and multiple exposures represents an attempt to circumvent such a problem by exploiting the following principle. Consider the formation of a focal-point image using an optical system and a non-linear photosensitive material in which m=2, as described above. In such an instance, the focal intensity distribution F(x) caused by the optical system can be considered independently from the illumination conditions. If the desired light-intensity distribution I.sub.0 (x) at the object is formed by overlaying focal images, then the latent image density distribution J(x) formed thereby is an accumulation of the light intensities created by the formation of each individual focal image, and is expressed by the following equation: EQU J(x)=I.sub.0 (x)*F(x).sup.2. (10)
The latent-image density distribution of the focal image is expressed in Equation (10) as F(x).sup.2, which has more amplitude than the focal-image intensity distribution F(x) created by the optical system. Thus, higher resolution is obtained.
The following equation is obtained by a Fourier transformation of Equation (10):
j(.nu.)=i.sub.0 (.nu.).multidot.[f(.nu.)*f(.nu.)]. (11)
When Equation (11) is compared with Equation (7), the "f*f" term in Equation (11) can be regarded as the OTF of the optical system. The cut-off frequency of the optical system, according to Equation (4), is 4NA/.lambda.. This cut-off frequency is double the cut-off frequency of the OTF expressed in Equation (7). Consequently, a doubling of the resolution is achieved.
In the method disclosed in Japan Kokai patent document no. HEI 6-291009, resolution is controlled by the exponent denoting the non-linearity of the photosensitive material. In order to double the resolution, a photosensitive material must be used that is non-linear wherein m.gtoreq.2, e.g., a "two-photon absorbing resist". However, the sensitivity of conventional non-linear photosensitive materials is low and these materials have an extremely high optical density (Optical Density (OD)=log(I/I.sub.0), where I.sub.0 and I represent the intensity of light incident to and passing through the photosensitive material, respectively). Consequently, an exposure light source and optical system with extremely high intensity must be used to elicit the desired non-linearity from the photosensitive material, which is impractical. In addition, since multiple repeated exposures are performed, each new exposure is considerably affected by the immediately preceding exposure.